Term for men in their twenties or thirties?

According to Wikipedia, "young adult"hood for psychologists is in the neighborhood of 20-39/40 year-olds, which would fit your student's population fairly well. There is clearly some variability; in addition to that pointed out in the article, for example, the American Psychological Association considers 18-29 to be the young adult age group, and 30-39 is called thirties, in its PsycINFO database. However, I think if the term were defined up front, it would be well understood (and clearly does not include younger teens).

I would therefore suggest Young adult males (this sounds better to me than young adult men, since the sexes are generally divided into male and female—see "Population" in the document linked above).